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Frequency-domain full-waveform inversion (FWI) is suitable for long-offsetstationary-recording acquisition, since reliable subsurface models can bereconstructed with a few frequencies and attenuation is easily implementedwithout computational overhead. In the frequency domain, wave modelling is aHelmholtz-type boundary-value problem which requires to solve a large andsparse system of linear equations per frequency with multiple right-hand sides(sources). This system can be solved with direct or iterative methods. Whilethe former are suitable for FWI application on 3D dense OBC acquisitionscovering spatial domains of moderate size, the later should be the approach ofchoice for sparse node acquisitions covering large domains (more than 50millions of unknowns). Fast convergence of iterative solvers for Helmholtzproblems remains however challenging due to the non definiteness of theHelmholtz operator, hence requiring efficient preconditioners. In this study,we use the Krylov subspace GMRES iterative solver combined with a multi-leveldomain-decomposition preconditioner. Discretization relies on continuous finiteelements on unstructured tetrahedral meshes to comply with complex geometriesand adapt the size of the elements to the local wavelength ($h$-adaptivity). Weassess the convergence and the scalability of our method with the acoustic 3DSEG/EAGE Overthrust model up to a frequency of 20~Hz and discuss its efficiencyfor multi right-hand side processing.

Iterative frequency-domain seismic wave solvers based on multi-level domain-decomposition preconditioners